Vector A has a magnitude of 18 (in some unspecified units) and makes an angle of 25 with the x axis, and a vector B has a length of 24 and makes an angle of 70 with the x axis. Find the components of the vector C in the following:

Question

(a) C = A + B
Cx =
Cy =
(b) C = A - B
Cx=
Cy=

Answer 1

(a) θ=25° φ=70°
Cx = Ax + Bx = |A|cos(θ) + |B|cos(φ)
=18cos(25)+24cos(70)
= 16.31 + 8.21
= 24.52

Cy = Ay + By = |A|sin(θ) + |B|sin(φ)
= 18sin(25)+24sin(70)
= 7.61 + 22.55
= 30.16

(b) similar to (a), but subtract instead of add.